Subgroups — #46808939

Order 34432.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31771010	C₂	1	1	yes	maximal, characteristic
2	#31770358	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₁₆×C₂₆₉	C₂	1	1	yes	maximal, characteristic
4	#22575453	—	2	1	no	—
5	#22575387	—	2	1	no	—
6	#22575387	C₄	1	2	yes	—
7	C₄⋊#14524130	—	2	1	no	—
8	C₂×C₁₆×C₂₆₉	—	2	1	no	—
9	C₄×C₈×C₂₆₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₅₃₈	—	4	1	no	—
11	C₂×#14524130	—	4	1	no	—
12	C₄⋊Dic₂₆₉	—	2	2	no	—
13	C₄⋊Dic₂₆₉	—	4	1	no	—
14	C₂×C₈×C₂₆₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₂₆₉	D₄	1	1	yes	characteristic
16	C₄²×C₂₆₉	D₄	1	1	yes	characteristic
17	C₁₆×C₂₆₉	—	4	1	no	—
18	Dic₅₃₈	—	8	1	no	—
19	Dic₅₃₈	—	8	1	no	—
20	C₂×Dic₂₆₉	—	4	2	no	—
21	#14524130	—	8	1	no	—
22	C₂×C₄×C₂₆₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₂₆₉	D₈	1	1	yes	characteristic
24	C₂×C₄×C₂₆₉	SD₁₆	1	1	yes	characteristic
25	C₈×C₂₆₉	—	2	1	no	—
26	C₈×C₂₆₉	SD₁₆	1	1	yes	characteristic
27	C₈×C₂₆₉	Q₁₆	1	1	yes	characteristic
28	C₂²×C₂₆₉	#102	1	1	yes	characteristic
29	C₄×C₂₆₉	—	2	1	no	—
30	C₄×C₂₆₉	#101	1	1	yes	characteristic
31	C₄×C₂₆₉	#103	1	1	yes	characteristic
32	C₄×C₂₆₉	D₁₆	1	1	yes	characteristic
33	C₄×C₂₆₉	SD₃₂	1	1	yes	characteristic
34	Dic₂₆₉	—	8	2	no	—
35	C₂×C₂₆₉	#332	1	1	yes	characteristic
36	C₂×C₂₆₉	#357	1	1	yes	characteristic
37	C₂×C₂₆₉	#362	1	1	yes	characteristic
38	C₂₆₉	#1364	1	1	yes	characteristic, complemented, Sylow
39	#1364	—	269	1	no	maximal, Sylow
40	#500	—	269	1	no	—
41	C₄⋊C₁₆	D₂₆₉	1	1	yes	characteristic
42	#335	—	269	1	no	—
43	C₄⋊Q₈	—	538	1	no	—
44	C₂×C₁₆	—	2	1	no	—
45	#107	—	269	2	no	—
46	#107	—	538	1	no	—
47	C₄⋊C₈	—	538	1	no	—
48	C₄×C₈	C₂×D₂₆₉	1	1	yes	characteristic
49	C₂×Q₈	—	1076	1	no	—
50	C₂×C₈	—	1076	1	no	—
51	C₂×C₈	C₄×D₂₆₉	1	1	yes	characteristic
52	C₂×C₈	C₂²⋊D₂₆₉	1	1	yes	characteristic
53	C₄⋊C₄	—	538	2	no	—
54	C₄⋊C₄	—	1076	1	no	—
55	C₄²	D₁₀₇₆	1	1	yes	characteristic
56	C₁₆	—	4	1	no	—
57	Q₈	—	2152	1	no	—
58	Q₈	—	2152	1	no	—
59	C₂×C₄	—	1076	2	no	—
60	C₂×C₄	#16864379	1	1	yes	characteristic
61	C₂×C₄	D₂₁₅₂	1	1	yes	characteristic
62	C₂×C₄	#16864391	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	2152	1	no	—
65	C₈	#16864390	1	1	yes	characteristic
66	C₈	#16864392	1	1	yes	characteristic
67	C₂²	#22575375	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	2152	2	no	—
70	C₄	#22575371	1	1	yes	characteristic
71	C₄	#22575376	1	1	yes	characteristic
72	C₄	D₄₃₀₄	1	1	yes	characteristic
73	C₄	#22575398	1	1	yes	characteristic
74	C₂	#31770350	1	1	yes	characteristic
75	C₂	#31770407	1	1	yes	characteristic
76	C₂	#31770422	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#22575375
commutator	C₂×C₈×C₂₆₉	C₂×C₄
Frattini	C₄×C₈	C₂×D₂₆₉
Fitting	C₄⋊C₁₆×C₂₆₉	C₂
socle, prime radical	C₂²×C₂₆₉	#102
cosocle	C₄×C₈×C₂₆₉	C₂²
hypercenter	C₄⋊C₁₆	D₂₆₉
hypocenter	C₂₆₉	#1364
LCS	G ▷ C₂×C₈×C₂₆₉ ▷ C₂×C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
38. C₂₆₉	#1364	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#31771010	2
#31770358	2
C₄⋊C₁₆×C₂₆₉	2
#1364	269